Answer to Question #204200 in Algebra for ACCORDANCE

Question

Consider the following examples in real-world situations that describe a correspondence between phenomena:

• The total cost for repairing a cell phone is R320 for parts plus R50 per hour for labour.

• Siphokazi sells 70% alcohol-based hand sanitisers. She earns R230 a week and receives a commission of 15% of her sales.

• The amount by which your savings will grow in a year depends on the interest offered by the bank.

• The area of a circle depends on the radius of the circle.

• A rental van costs R230 per day plus R4,30 per kilometre.

(a) Express each situation in functional words. For example, the income tax is a function of the total income. (8)

(b) For each situation, indicate the dependent and independent variables. (5)

(c) Write the two variables as an ordered pair, and write the function using the notation 𝑦=(𝑥). (5)

(d) Explain the meaning of a function in your own words. Illustrate with your own specific example. (2)

Answer 1

a)

• Total cost is a function of the labour of repairing a cellphone.
• The earning by siphokazi is a function of her commission.
• Amount is a function the interest offered by the bank.
• The rental amount of a van is a function of kilometers travelled.

B)

• Total cost is dependent while labour is independent.
• Earnings are dependent while commission is Independent.
• Amount is dependent and interest offered by the bank is independent.
• The rental amount of a van is dependent while kilometers travelled is independent.

C) the two variables ( both the dependent and the I dependent ) are represented by x and y. So, the function of the two variables is shown by;

Function f(x,y)

D) A Function can be defined as a relation between two sets that tries to associate every element of the first set to exactly one element of a second set.

Example.

F(x)= x² +2

And

G(x) = 3x+7